“On
Gauss' class number problem”
Abstract
Gauss
conjectured that his tables of class numbers published in the Disquisitiones
Arithmeticae in 1801 were complete and that there should be an effective
algorithm to determine all imaginary quadratic fields with a given class number.
While visiting Pisa, 1974-1975, I showed that Gauss' conjecture could be reduced
to a special case of the Birch-Swinnerton-Dyer conjecture on elliptic curves.
This conjecture was solved by Gross-Zagier in 1984 and then the three of us won
the Cole Prize in number theory shortly after that for the solution of Gauss'
conjecture on class numbers. This talk will outline the history of the problem
and some ideas of the solution.
ore
17.00
Aula
Mancini
Palazzo
della Carovana
Piazza
dei Cavalieri, 7
PISA